Prior art communication receivers use digital signal processing (DSP) for many of the basic receiver functions such as frequency translation, filtering, and demodulation. See for example, U.S. Pat. No. 4,592,074 which uses DSP for frequency translation and filtering. In general, DSP permits receivers to be designed with higher performance, accuracy, and flexibility.
FIG. 1 is a block diagram of a prior art FM receiver, with signal demodulation and other functions performed by DSP. Analog front end circuitry processes the signal received at the antenna and inputs the processed analog signal to an analog-to-digital converter (A/D), which digitizes the signal. The analog processing may include gain, frequency translation, and filtering. The digital output of the A/D converter is processed by DSP circuitry that may perform gain, frequency translation and filtering functions in the digital domain to isolate the signal in the desired receiver channel. The desired signal is then input to the FM demodulator, which outputs the baseband signal, which is the FM composite signal for standard FM broadcast.
FM can be described mathematically as phase modulation of a carrier by the integral of the modulating (or baseband) signal, as discussed in Solid State Radio Engineering, by Krauss, Bostian, and Raab, published by John Wiley and Sons, 1980. Thus, the demodulation process for FM can be described as the derivative of the phase of the modulated carrier.
It is common in DSP-based receivers to process the receive signal in complex from, i.e. with real (in-phase or I) and imaginary (quadrature-phase or Q) components. In general, using a complex representation has advantages in frequency translation and demodulation, and allows sample rates to be reduced. A single carrier in complex form can be represented diagrammatically as a single phasor in the real-imaginary signal plane, with the real and imaginary coordinates of the phasor's tip equal to I and Q respectively, as shown in FIG. 2. The magnitude M of the carrier is the length of the phasor, and the phase of the carrier is the angle P from the real axis, as shown. Thus, one prior art FM demodulation scheme is to calculate the phase equal to the arctangent of Q divided by I, then take the derivative of the phase to obtain the baseband signal. This scheme has two problems: calculation of arctangent is difficult, and the arctangent function in general gives a result that is discontinuous due to wrap around from +pi to -pi and vice-versa. It can be easily shown using standard derivative tables that the derivative of the arctangent of Q divided by I can be simplified to the following function. ##EQU2## where S(t)=desired baseband signal,
I(t)=in-phase carrier component, PA1 Q(t)=quadrature-phase carrier component.
The denominator of (1) is the square of the magnitude of the carrier phasor. The magnitude of the phasor is the square-root of the sum of the squares of I(t) and Q(t), and can also be considered the norm of the vector [I(t) Q(t)]. If K is defined as the inverse of the magnitude, and if I.sub.1 (t)=KI(t) and Q.sub.1 (t)=KQ(t), then (1) can be re-written as follows. ##EQU3##
Equation (2) can be viewed as the modified demodulator. The magnitude of the phasor formed by I.sub.1 (t) and Q.sub.1 (t) is exactly 1 due to the value of K. Thus, multiplying I (t) and Q(t) by K to obtain I.sub.1 (t) and Q.sub.1 (t) in effect "normalizes" the phasor to magnitude 1. This removes any amplitude variation of the carrier phasor, and thus performs the same function as a limiter in an analog FM demodulator.
The demodulation process thus consists of normalizing the complex signal, then using the modified demodulator to demodulate the normalized signal, as shown in FIG. 3. Normalization is performed by calculating K as defined above, and then multiplying I and Q by K. The derivatives in (2) (as well as in (1)), can be calculated using known methods, such as FIR or IIR filter structures.
K can be calculated from a polynomial function of I.sup.2 +Q.sup.2. However, many terms, and thus multiplications, are needed for high accuracy of K. Alternatively, the square root of (I.sup.2 +Q.sup.2) can be calculated using a square-root algorithm, such as a polynomial algorithm or Booth's algorithm. Then K can be calculated using a 1/x function, such as binary long division. Still another method is to use Newton-Raphson iteration. In terms of hardware or software implementations, all of these approaches require an excessive amount of processing power to obtain K.
In accordance with the present invention a method and apparatus is provided which arrives at a value of K in a iterative manner, which in relation to the prior art requires a smaller amount of processing power, thus reducing the cost of implementing the function.